Low-loss,low-distortion transmission lines



April 15, 1969 R. c. LEVINE 3,439,120

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LOW-LOSS, LOW-DISTORTION ramsmssxou LINES April 15, 1969 Sheet 5 of3Filed May 1, 196? United States Patent 0 3,439,120 LOW-LOSS,LOW-DISTORTION TRANSMISSION LINES Richard C. Levine, Plainfield, N.J.,assignor to Bell Telephone Laboratories, Incorporated, Berkeley Heights,

N.J., a corporation of New York Filed May 1, 1967, Ser. No. 635,126 Int.Cl. H01b 11/16 US. Cl. 178-45 13 Claims ABSTRACT OF THE DISCLOSURELow-distortion, low-loss transmission is achieved by terminating atransmission line, whose distributed parameters are a per-unit-lengthseries impedance z, and a perunit-length shunt admittance y, with aterminating impedance Z equal to zv/jw where v is a convenient wavepropagation speed, and by shunting the line at substantially equaldistances x, with respective admittances Y each equal to [z/Z y]x.

BACKGROUND OF THE INVENTION Field of the invention This inventionrelates to wave transmission networks and particularly to communicationcables Whose transmission lines incorporate means for transmittingcommunication signals with little distortion or loss.

Description of the prior art Past attempts at reducing distortion andloss in a transmission line have involved adding series inductors orseries negative resistances at intervals along the transmission line.Both expedients have served mainly to reduce the ratio of the linesseries resistivity R to the lines inducti-vity, that is its inductanceper unit length, L They there fore effectively reduced the linesattenuation. Moreover, by making the ratio R /L approach the usuallysmall ratio G /C of the lines shunt conductivity to shunt capacitance,they reduced the problems arising from the irrational frequencyfunctions which otherwise characterize the lines characteristicimpedance Z and its propagation constant With modern requirements forgreater transmission capacity, these efforts have been found wanting.Inductors produce destructive interference when the signal wavelength isapproximately four times the inductor spacing. At this wavelength thecombination of lines and inductors act as a low-pass wave filter. On theother hand, negative series resistances, to be fully effective inreducing loss and distortion, require lines whose matched terminationsare purely resistive. In practical systems, gain is sacrified toaccommodate reactive terminations. Thus to this time, combinations ofthese expedients have failed to yield the desirable combination oflow-loss, low-distortion transmission for reactive terminations.

THE INVENTION According to the invention low-distortion and low-loss isachieved in a transmission line, by keeping the line free of seriesimpedances and shunting the line periodically with negative impedanceshunt loading networks each of which balances out the lines existingper-unit-length admittance y and at the same time establishes in itsstead another net admittance that supplements the signal energy in theline and varies the phase of the signal so that it tends to rise morelinearly with frequency. According to a more particular feature of theinvention the other admittance is such as to modify the linesper-unit-length admittance toward that required for anideally-terminated 3,439,120. Patented Apr. 15, 1969 ideal losslessdistortionless transmission line, namely one where /z/y=Z =Z and /zy=jw/v. In these formulas z is the per-unit-length loop impedance of theline, Z is the lines characteristic impedance, Z is its terminatingimpedance and v is any one of a range of real propagation speeds lessthan the lines intrinsic wave speed.

According to a still more specific feature, low-distortion, low-losstransmission is achieved by making the new admittance equalsubstantially to Z/ZT2, where Z =zv/jw. By virtue of the invention,low-loss, low-distortion transmission is achieved with a wide range ofterminations for any particular line. The terminations values dependmainly on the series loop impedance per-unit-length without dependingupon the shunt admittance per-unit-length.

According to another more specific feature of the invention,particularly where skin effect is negligible, a transmission line, whoseper-unit-length parameters include a resistivity R; an inductivity L acapacitance C and a conductivity G is made distortionless by terminatingit with a resistance R equal to L v wherein v equals a suitably selectedpropagation speed and a series capacitance C equal to l/R v, and byperiodically shunting the line at distances x with a capacitor [1/R v-C]x in parallel with a resistor 1/G x and a series network having aresistance R C v/x and a capacitance x/R v.

These and other features of the invention are pointed out in the claims.Other advantages and objects of the invention will become evident fromthe following detailed description when read in light of theaccompanying drawings:

DESCRIPTION OF THE DRAWINGS FIG. 1 is a partially schematic blockdiagram illustrating a communication transmission system embodyingfeatures of the invention;

FIG. 2 is a schematic diagram illustrating the lumped parameterequivalent circuit of a transmission line segment in FIG. 1;

FIG. 3 is a partly schematic diagram illustrating a communicationtransmission system like that of FIG. I having another transmission lineand also embodying features of the invention;

FIG. 4 is a schematic diagram illustrating another lumped parameterequivalent circuit of a transmission line segment of the line of FIG. 1;

FIG. 5 is a schematic diagram of another shunt network suitable for thelines of FIGS. 1 and 3; and

FIG. 6 is a partially schematic 'block diagram illustrating anothertransmission system, similar to that of FIG. 1, and also embodyingfeatures of the invention.

DESCRIPTION OF THE EMBODIMENTS In FIG. 1 two insulated conductors CO1and CO2, among many such insulated conductors CO in a telephonedistribution cable CA, form a transmission line TR among many such linesTRN. The cable CA is composed of longitudinally sequential cablesegments SE having substantially equal lengths x which are joined bysplices SP. Within the splices SP suitable connectors Con join thesequential wire segments that make up the respective conductors C01, C02and CO. The transmission line TR ends at telephone set TS having aterminating impedance Z The terminating impedance Z is composed of aresistive portion R and a capacitive portion C The The transmission lineTR, together with the other lines TRN, starts in a telephone centraloffice TCO. In the office TCO a source SO, exhibiting to the line TR animpedance equal to that of the terminating impedance Z transmitselectrical communication signals along the lines CO1 and CO2. It alsosupplies a direct voltage across the lines CO1. and CO2 so that theconductor 3 CO1 is positive relative to the conductor CO2. Periodicallyshunting the connectors Con in the conductors CO1 and CO2 and pairs ofthe conductors C0, are a plurality of shunt networks SN.

The transmission line TR when otherwise not connected to load orcompensated by the networks SN exhibits a loop impedance composed of theimpedances of successive incremental line lengths, each of whichapproximates the impedance of the lumped parameter circuit C shown inFIG. 2. The shorter the incremental length considered the more closelysuccessive combinations of the circuit C approximate the impedance ofthe line TR. Thus the line TR exhibits a series loop impedanceper-unit-length z and a shunt admittance per-unitlength y. The per-unitimpedance 2 is composed of a resistivity or per-unit-length resistance Rand an inductivity or perunit-length inductance L The per-unitlengthadmittance y is composed of a shunt conductivity or per-unit-lengthconductance G and a shunt per-unitlength capacitance C The R of thetermination Z may have any value of R =L v, and the capacitance C anyvalue l/R v, where v is a speed conveniently selected from a range ofwave propagation speeds less than the intrinsic propagation speed l/ /LC of the transmission line TR. The value v is a scalar quantity andhence real. It is selected to make R and C convenient to the apparatusof which the termination Z is composed. The distance x between splicesis less than the longest distance over which the approximationrepresented by the lumped parameters of FIG. 2 is reasonable in terms ofthe highest frequency to be transmitted.

In FIG. 1, forming each of the shunt networks SN is a shunt capacitor SCwhose value is x/R v. Connected parallel across the capacitor SC is anegative impedance converter NIC that terminates in an impedance Z. Anyone of a number of negative impedance converters may be used.

Forming the illustrated negative impedance converter NIC is a high 13PNP transistor Q1 whose collector is biased from the negative conductorCO2 through a resistor r and whose emitter connects to the positiveconductor CO1. Feeding the base of the transistor Q1 is the collector ofa high 3 transistor Q2 whose own emitter is connected to the conductorCO2 and whose own base receives signals fed back from the collector oftransistor Q1 through a resistor R whose value is n-r. The impedanceexhibited by input of the negative impedance circuit over a suitablerange equals the negative of Z/n, namely --Z/n. The operation of theillustrated negative impedance converter is described fully in theTechnical Report of Minoro Nagata No. 4813-5 prepared under Ofiice ofNaval Research Contract Nonr-225 (44), NR 375865 by the Solid StateElectronics Laboratory, Stanford Electronics Laboratory, StanfordUniversity, Stanford, Calif. No. SEL-65-037.

The impedance Z is composed in part of a resistor R whose value is equalto n/G x and a capacitor C equal to nC x. Since the impedance exhibitedby the negative impedance converter NIC is the negative of the impedance2/11 the effects of the resistor R and capacitor C are to balance outthe positive shunt conductivity G and the positive shunt capacitance Cover the distance x of the transmission line TR. The impedance Z alsoincludes in parallel with the resistor R the resistor RN and a capacitorCN in series therewith. The values of the resistor RN are equal to R Cv/xn. The value of the capacitor CN is equal to nx/R v. This resistorand capacitor thus establish across the line an additional negativeimpedance that changes the admittance of the line TR. In fact, togetherwith the capacitor SC the admittance across the line corresponds to thatof a capacitor connected across the line having a value x/R v andaseries RC circuit composed of a resistance equal to -R C vx and acapacitance -x/R v.

Since capacitors SC and C are subtractive, a single capacitor may besubstituted for their combination at either the input or output of theconverter NIC depending upon the resulting sign when the capacitancevalues are subtracted.

A general qualitative appreciation of the operation of FIG. 1 can beobtained by considering a signal transmitted by the source SO along theline TR. That signal reaches a network SN in somewhat attenuated formdue to the lines intrinsic impedance z and admittance y. The network SNresponds by reflecting part of the waveform in both directions. However,by virtue of its negative impedance the energy of the reflected wave canbe greater than the arriving wave. The network SN supplements the energypassing the network SN so that the latter exceeds the arriving energy.By virtue of the relation of the networks components to the phase of theincoming signal the phase of the passing signal is changed to besubstantially linear with frequency. At the same time, because of thephase shift, the reflective wave avoids strong destructive interferenceeffects. Thus attenuation and distortion of the line TR aresubstantially reduced at each network SN. The networks SN are such as tosupplement the signals and phase them so they appear to be encounteringa substantially lossless and distortionless line.

A more qualitative and rigorous explanation is available by consideringthe circuit of FIG. 2. In operation when uncompensated as shown in FIG.2, the intrinsic distributed per-unit-length impedances z and per-unitlength admittances y of the line TR distort and attenuate signalsgenerated by the source S0. The distance x is small enough so that theapproximations represented by FIG. 2 are valid. Then the networks SN atintervals x change the per-unit-length admittance y of the line TR. Ineach network SN the resistors R whose values are n/G x and which areformed by the negative impedance converters into values -1/G x balancethe values of the conductances G x for each line segment over which G ismeasured. The capacitors C in each network SN similarly balance andpractically eliminate the effect of the capacitance C in each linesegment. Moreover, the capacitors SC of each network SN and the membersRN, and CN introduce over any distance x capacitances across the linehaving the valuel/R v and series RC circuits across the line whoseresistance values are R '-C v and whose capacitive values are 1/R v. Theresulting total admittance y of the shunt network SN and its associatedline segment over a distance x equals At the same time the terminatingimpedance Z has a value R +l/jwC- where R =vL and C =l/vR Theterminating impedance Z and the shunt networks when placed atcomparatively short intervals along the line, closely approximate thecondition for a distortionless lossless line, namely that #57: 10/ v,and VW=Z This becomes evident from replacing R and C in y with theirvalues in terms of R and L This condition defines an attenuationlessline. Moreover,

Z =R +1/jwC Substituting for R and C their respective values T= L L i (jL'i L) However, fwL +R =Z and v/jw=1/ /R But x/z/y' is thecharacteristic impedance Z of the line and hence the line is terminatedfor minimum distortion or reflection of the signal.

The general conditions for a lossless distortionless line exist whenThis is so because y=z/ (Z v /j w 'Thus fi=jw/ v. This satisfies onecriterion. Now

This satisfies the other criterion for a lossless distortionless line.

In effect therefore the network SN modifies the admittance y to a valuenecessary for conforming to the conditions for a distortionless line'with an ideal terminating impedance. Thus waveforms emerging from thesource SO encounter an almost ideal lossless distortionless line.

In FIG. 1 the networks SN shunt line TR without intervening seriesloads. Thus the network SN is always balanced with respect to theconductor CO1 and CO2. Furthermore, the shunt network SN is affectedonly by differences in voltage between the conductors. Therefore,lightning surges or induced power line voltages affecting the conductorsCO1 and CO2 equally do not flow through the networks SN and are notamplified by them. As shown in FIG. 1 the shunt networks are used inexisting conventional cable systems by connecting them 'between theconductor connectors that join sequential lengths of respectiveconductors in cable splices. This greatly improves the usable bandwidthof existing equipment. Moreover, the simplicity of the circuits in theshunt networks SN permits integrating the shunt networks into the cablesheath along with the conductor pairs. Present techniques of integratedcircuitry make this possible. As a result, thinner copper wires or wiresof metals having higher resistivities at lower costs are feasible. Acable using circuits integrated into the line is shown in the system ofFIG.. 3, where conductors CO1 and CO2 comprise wires W having networksSN of integrated structure connected between them at suitable intervalsunder the insulation I which surrounds the wires W to form twisted pairsp.

The shunt networks SN, by eliminating the need for series impedances inthe line, permit free flow of direct currents for energizing thenegative impedance converters NIC. As a result, no supplementary directpower is necessary in transmission lines TR.

The invention is applicable even at those high frequencies above whichindividual line segments can be considered as presentable by the lumpedparameter illustrated in FIG. 2, mainly by the values L R C and 6 Thatis to say, the invention may be extended to the range of frequencies atwhich skin effect becomes important. At these frequencies line segmentshave the characteristics of the circuits of FIG. 4. Here, the resistorsR RL2, RL3, inductors LLI, LL2, LL3, capacitors GL1, GL2, C andconductances G G G present a more complex pattern. However, as long as Z=zv/jw, and in each network SN the net y'=xz/Z that is y issubstantially equal to [z/Z -y]x-yx, signals leaving the source SOencounter an essentially lossless line. Since v is speed, a. scalarquantity, it must be real.

An example of a circuit utilizing this more general condition appears inFIG. 5. This corresponds substantially to the circuit of FIG. 1.However, the impedance Z here includes a circuit portion generallydesignated y Whose admittance equals yx and a circuit portion whose netadmittance equals xz/Z FIG. 5 corresponds otherwise to FIG. 1. FIG. 1thus represents a more specific embodiment of the general form in FIG.5.

FIG. 6 illustrates .a system, corresponding to that of FIG. 1, whereinwires separate from the transmission lines furnish the direct currentfor operating the negative impedance converted in each shunt network SN.In such a system a single heavy pair of lines DCWI and DCW2 efficientlyfurnish the needed direct current to all the shunt networks. Thetransmission lines C0, C01 and CO2 then need only be heavy enough tocarry the communications signals. FIG. 6 utilizes in place of convertersNIC negative impedance converters NIC2 that separate direct-currentlines DCWI and DCW2 from the signal lines C0, C01 and CO2. This preventssignals from passing along the direct-current lines. The negativeimpedance converters are the type disclosed in June 1953 Pro ceedings ofthe Institute of Radio Engineers, Volume 41, pages 725 et seq. by I. G.Linville. They require splitting the members in the impedance Z so thatthe elements therein have the values shown with respect to the values inFIG. 1. The value n appears in FIG. 6 since the comparison is made toFIG. 1. In FIG. 1 n=R/ r represents a conversion factor for the negativeimpedance converter. In FIG. 6 the circuit NIC2 has a unity conversion.The comparison is simpler if, in FIG. 1, n is made equal to 1.

While embodiments of the invention have been described in detail, itwill be obvious to those skilled in the art that the invention may beotherwise embodied without departing from its spirit and scope.

What is claimed is:

1. A circuit for connection across the conductors of a transmission lineterminated at each end by coresponding termination impedances,comprising negative impedance converter means having an input side andan output side and exhibiting at its output side the negative of theimpedance appearing at its input side, conductive means connecting saidoutput side of said negative impedance converter means between saidconductors, impedance means connected to said negative impedanceconverter means for establishing an impedance between said conductivemeans that changes the total admittance of the line over a predetermineddistance along the line toward a value which is the quotient of theseries impedance of the line over the predetermined distance divided bythe square of the terminating impedance.

2. A device as in claim 1 wherein said impedance means include firstimpedance means on the input side of said negative impedance convertedmeans and second impedance means on the output side of said negativeimpedance converter.

3. A device as in claim 1 wherein said impedance converter means includea first impedance network having a value equal to the line admittanceover the predetermined length and connected to the output side of thenegative impedance converter means and a second impedance networkconnected to one of the sides of said negative impedance converter.

4. A device as in claim 1 wherein the predetermined distance is x, andsaid impedance means form with said negative impedance converter means acapacitance x/R v-xC and further include across the input side of saidnegative impedance converter means a resistance 1/ G x and a seriesnetwork having a resistance R C v/ x and a capacitance x/R v, where Cand G are the capacitance of the line over the distance x and R and Care the series resistance and capacitive components of said terminatingimpedance and wherein v=R /L =C R L and R being the respective seriesinductance and series resistance of the line over the distance z.

5. A device as in claim 1 wherein said impedance means and saidconverter means change the value of the admittance of said line over thepredetermined distance x from its capacitance C and conductance G towarda total value represented by a shunt capacitor having a value x/R v anda shunt circuit composed of a series resistor -R C- -v/x and a seriescapacitor x/R v wherein R and C represent the series resistance andseries capacitance of said terminating impedance and v=R /L C R R and Lbeing the loop resistance and loop inductive over the line over thedistance x.

6. A transmission system, comprising a transmission line having asubstantially uniform distributed loop impedance per-unit-length of zand loop admittance per-unitlength y, terminal means at each end of saidline having a value Z a plurality of negative impedance converter meanseach having an input and an output and exhibiting at said output thenegative of the impedance at said input, conductive means on each ofsaid negative impedance converter means for connecting the output ofsaid negative impedance converter means across said line at spacedperiodic locations, impedance means connected to each of said negativeimpedance converter means for establishing therewith an impedancebetween said conductive means that changes the total admittance y over aportion of the line equal to the distance between locations toward avalue z/Z 7. A transmission system as in claim 6 wherein said lineincludes a plurality of connected line segments with connector meansjoining said segments, and wherein said conductive means connect saidnegative impedance converter means across said conductive segments.

8. A transmission system as in claim 6 wherein said line includes twoconductors and each of said converter means and each of said conductivemeans form a part of respective integrated circuits connected betweenthe conductors of said line.

9. A transmission system as in claim 6 'wherein said impedance meansinclude first impedance means on the input side of said negativeimpedance converter means and second impedance means on the output sideof said negative impedance converter.

10. A transmission system as in claim 6 wherein said impedance convertermeans include a first impedance network having an admittance equal tothe line admittance over the predetermined length and connected to theoutput side of the negative impedance converter means and a secondimpedance network connected to one of the sides of said negativeimpedance converter.

11. A transmission system as in claim 6 wherein said conductive meansconnecting said converter means are separated from each other by adistance x and :wherein said impedance z per-unit-length is approximatedby a series resistance per-unit-length R and a series inductanceper-unit-length L said admittance per-unit-length y being approximatedby a per-unit-len'gth conductance G and capacitance C said terminalmeans Z being composed of a series resistance R and a series capacitanceC said impedance means forming with said converter means a capacitancex/R vxC and further including across the input of said converter means aresistance 1/ G and a series network having a resistance R C v/x and acapacitance x/R v, wherein v=R /L =C /R 12. A transmission system as inclaim 6 wherein said conductive means connecting said converter meansare separated from each other by a distance x and wherein said impedancez per-unit-length is approximated by a series resistance per-unit-lengthR and a series inductance per-unit-length L said admittanceper-unit-length y being approximated by perunit-length conductance G andcapacitance C said terminal means Z being composed of a seriesresistance R and a series capacitance C said impedance means and saidconverter means changing the value of the total admittance of said lineover the distance x from its capacitance C and conductance G;, toward atotal value represented by a shunt capacitor having a value x/R- v and ashunt circuit composed of a series resistor -R C- v/x and a seriescapacitor -x/R v,

13. A system as in claim 6 wherein separate lines furnish power to saidnegative impedance converter means.

References Cited UNITED STATES PATENTS 2,933,703 4/1960 Kinariwala 333-HERMANKARL SAALBACH, Primary Examiner.

P. L. GENSLER, Assistant Examiner.

US. Cl. X.R.

